Controllability For Schr(?)dinger Equation

In this article we report some existing results on the controllability of Schrodinger equa-tion. This has been a topic of research in which very intensive work has been done by many authors in the last twenty years.In section 1, we reduce the Schrodinger equation, and give some explains about its solution.In section 2, we give some results about the solution of Schrodinger equation, such as the uniqueness of the solution and Strichartz's estimates. We also give some other results about variational approach.In section 3, firstly, we discuss the controllability of the linear Schrodinger equation with a boundary control by HUM (Hilbert Uniqueness Method) and Multiplier techniques; secondly, we discuss the controllability of the linear Schrodinger equation with a control distributed along a sub domain of the domain where the equation holds; finally, we de-scribe the existing positive and negative results on this matter.In particular, we shall talk about Geometric Control Condition in detail.In section 4, we shall briefly comment on the controllability of semi linear equations with an interior control. We shall introduce a method which is used to solve the control-lability of semi linear wave equation by Zuazua. We shall mention some interesting open problems. Finally, we shall show a recent result about the local controllability,and some method used to solve the problem.